ESL jobs and ESL employers can be as varied abroad as employers are in your country, however...
This photo contains a bit of humor and a kernel of truth. In most situations a degree is the requirement, but after the degree comes some other said qualifications. I can't say it's like this all across the board, but I can say that many schools do operate like this.
It may be more common in the private school sector like in: buxibans, eikaiwa, hagwans, and training centers and sometimes less common in public schools and universities.
In the west no one will put in a job advertisement that they're looking for someone who is attractive and charismatic. I mean there are laws against workplace discrimination.
But does it not play a role?
You won't see those two words listed in a job advertisement in Asia either. Yet you will find some job advertisements that say they are looking for a Caucasian, female or perhaps young teacher. You can read more about those in ESL employer preferences.
Here Uncle Chang puts attractiveness and charisma high upon his list and gives each factor a value of +3.
Factors that contribute to you finding a job teaching ESL at many schools in Asia
Attractiveness
No one wants to say that it matters, but they don't have to, they'll just ask for your photo instead. If it didn't matter then no employer would request a photo with your resume, but nearly everyone does. A preference for race, sex and age can all come into play here. If you're handsome or pretty and you find yourself working in a private school or even at university you could find your photo gracing billboards around town.
Charisma
If you can get your foot in the door for an interview then this one will come into play. Your personality can be quite influential. And this can be the deciding factor.
Experience
Most schools will prefer a teacher with experience. And some will prefer the one with experience in their own country versus the one without in-country experience. Does it matter? Teaching English is teaching English right? I never thought so, but to some schools it does.
Certified Teachers, Master's Degree Holders & Other Specialized Majors
Certified teachers will get some perks. For example, in Taiwan you'll be able to work in a public school, non-certified teachers cannot. You'll also be able to teach in international schools throughout Asia.
It doesn't matter too much what you're certified to teach, what matters is that you will be defined as a proper "teacher". Master's degree holders will also be highly regarded and will able to teach in Universities in Japan and Taiwan.
In general English related degrees look good.
TEFL/TESOL Certification
A CELTA certificate may also be included with the above qualifications. Some schools may prefer that you have TEFL/TESOL certification, but in most of Northeast Asia it's not required. And in terms of helping you to get a job they can be the lowest common denominator.